Redfern was the son of former Sheffield Wednesday captain Frank Froggatt, and the cousin of England international Jack Froggatt. In 1942 'Red' was signed from Sheffield YMCA but did not become a regular player in the Wednesday side until 1945. Over the course of the next 15 years he would go on to make a total of 498 appearances for the club, mostly as a striker but playing over 50 games as a winger, scoring 149 goals. He made his England debut in a match against Wales in 1952 and in total received four England caps scoring 2 goals. His final game for Wednesday came in the 1959–60 season.